Living Rev. Solar Phys., 7, (2010), 1 LIVING REVIEWS http://www.livingreviews.org/lrsp-2010-1 in solar physics The Solar Cycle David H. Hathaway Mail Code VP62, NASA Marshall Space Flight Center, Huntsville, AL 35812, U.S.A. email: [email protected] http://solarscience.msfc.nasa.gov/ Accepted on 21 February 2010 Published on 2 March 2010 Abstract The Solar Cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. We examine a number of other solar activity indicators including the 10.7 cm radio flux, the total solar irradiance, the magnetic field, flares and coronal mass ejections, geomagnetic activity, galactic cosmic ray fluxes,and radioisotopes in tree rings and ice cores that vary in association with the sunspots. We examine the characteristics of individual solar cycles including their maxima and minima, cycle periods and amplitudes, cycle shape, and the nature of active latitudes, hemispheres, and longitudes. We examine long-term variability including the Maunder Minimum, the Gleissberg Cycle, and the Gnevyshev{Ohl Rule. Short-term variability includes the 154-day periodicity, quasi-biennial variations, and double peaked maxima. We conclude with an examination of prediction techniques for the solar cycle. This review is licensed under a Creative Commons Attribution-Non-Commercial-NoDerivs 3.0 Germany License. http://creativecommons.org/licenses/by-nc-nd/3.0/de/ Imprint / Terms of Use Living Reviews in Solar Physics is a peer reviewed open access journal published by the Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany. ISSN 1614-4961. 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Contents 1 Introduction 5 2 The Solar Cycle Discovered6 2.1 Schwabe's discovery...................................6 2.2 Wolf's relative sunspot number.............................7 2.3 Wolf's reconstruction of earlier data..........................7 3 Solar Activity Data9 3.1 Sunspot numbers.....................................9 3.2 Sunspot areas....................................... 11 3.3 10.7 cm solar flux..................................... 13 3.4 Total irradiance...................................... 14 3.5 Magnetic field....................................... 17 3.6 Flares and Coronal Mass Ejections........................... 18 3.7 Geomagnetic activity................................... 19 3.8 Cosmic rays........................................ 21 3.9 Radioisotopes in tree rings and ice cores........................ 24 4 Individual Cycle Characteristics 25 4.1 Minima and maxima................................... 25 4.2 Smoothing......................................... 28 4.3 Cycle periods....................................... 31 4.4 Cycle amplitudes..................................... 32 4.5 Cycle shape........................................ 33 4.6 Rise time vs. amplitude (The Waldmeier Effect)................... 34 4.7 Period vs. amplitude................................... 36 4.8 Active latitudes...................................... 36 4.9 Active hemispheres.................................... 37 4.10 Active longitudes..................................... 40 5 Long-Term Variability 42 5.1 The Maunder Minimum................................. 42 5.2 The secular trend..................................... 42 5.3 The Gleissberg Cycle................................... 43 5.4 Gnevyshev{Ohl Rule (Even{Odd Effect)........................ 43 5.5 Long-term variations from radioisotope studies.................... 44 5.6 The Suess cycle...................................... 44 6 Short-Term Variability 45 6.1 154-day periodicity.................................... 45 6.2 Quasi-biennial variations and double peaked maxima................. 46 7 Solar Cycle Predictions 47 7.1 Predicting an ongoing cycle............................... 47 7.2 Predicting future cycle amplitudes based on cycle statistics............. 47 7.3 Predicting future cycle amplitudes based on geomagnetic precursors........ 48 7.4 Predicting future cycle amplitudes based on dynamo theory............. 53 8 Conclusions 56 References 57 List of Tables 1 Dates and values for sunspot cycle maxima....................... 26 2 Dates and values for sunspot cycle minima. The value is always the value of the 13-month mean of the International sunspot number. The dates differ according to the indicator used..................................... 27 3 Dates and values of maxima using the 13-month running mean with sunspot number data, sunspot area data, and 10.7 cm radio flux data.................. 28 4 Dates and values of maxima using the 24-month FWHM Gaussian with sunspot number data, sunspot area data, and 10.7 cm radio flux data as in Table3..... 30 5 Cycle maxima determined by the 13-month mean with the International Sunspot Numbers and the Group Sunspot Numbers. The Group values are systematically lower than the International values prior to cycle 12.................. 32 6 Prediction method errors for cycle 19 { 23. The three geomagnetic precursor methods (Ohl's, Feynman's, and Thompson's) give the smallest errors............. 52 The Solar Cycle 5 1 Introduction Solar activity rises and falls with an 11-year cycle that affects us in many ways. Increased solar activity includes increases in extreme ultraviolet and x-ray emissions from the Sun which produce dramatic effects in the Earth's upper atmosphere. The associated atmospheric heating increases both the temperature and density of the atmosphere at many spacecraft altitudes. The increase in atmospheric drag on satellites in low Earth orbit can dramatically shorten the lifetime of these valuable assets (cf. Pulkkinen, 2007). Increases in the number of solar flares and coronal mass ejections (CMEs) raise the likelihood that sensitive instruments in space will be damaged by energetic particles accelerated in these events. These solar energetic particles (SEPs) can also threaten the health of both astronauts in space and airline travelers in high altitude, polar routes. Solar activity apparently affects terrestrial climate as well. Although the change in the total solar irradiance seems too small to produce significant climatic effects, there is good evidence that, to some extent, the Earth's climate heats and cools as solar activity rises and falls (cf. Haigh, 2007). There is little doubt that the solar cycle is magnetic in nature and produced by dynamo processes within the Sun. Here we examine the nature of the solar cycle and the characteristics that must be explained by any viable dynamo model (cf. Charbonneau, 2005). Living Reviews in Solar Physics http://www.livingreviews.org/lrsp-2010-1 6 David H. Hathaway 2 The Solar Cycle Discovered Sunspots (dark patches on the Sun where intense magnetic fields loop up through the surface from the deep interior) were almost certainly seen by prehistoric humans viewing the Sun through hazy skies. The earliest actual recordings of sunspot observations were from China over 2000 years ago (Clark and Stephenson, 1978; Wittmann and Xu, 1987). Yet, the existence of spots on the Sun came as a surprise to westerners when telescopes were first used to observe the Sun in the early 17th century. This is usually attributed to western philosophy in which the heavens and the Sun were thought to be perfect and unblemished (cf. Bray and Loughhead, 1965; Noyes, 1982). The first mention of possible periodic behavior in sunspots came from Christian Horrebow who wrote in his 1776 diary: \Even though our observations conclude that changes of sunspots must be periodic, a precise order of regulation and appearance cannot be found in the years in which it was observed. That is because astronomers have not been making the effort to make observations of the subject of sunspots on a regular basis. Without a doubt, they believed that these observations were not of interest for either astronomy or physics. One can only hope that, with frequent observations of periodic motion of space objects, that time will show how to examine in which way astronomical bodies that are driven and lit up by the Sun are influenced by sunspots." (Wolf, 1877, translation by Elke Willenberg) 2.1 Schwabe's discovery Although Christian Horrebow mentions this possible